[Vuejs]-How to push a history entry and change address bar url without navigating to that url?

Use Vue Router (google it) for this. Just keep in mind that stuff like this generally means a lot of work for very little gain.

With Vue Router you can set your app up so that page.com/book/Test directs you to page.com/book with the variable Test set.

I recommend setting your site up as a single file project using Webpack and the Vue plugin, and using that eith Vue router. Then you can get the functionality you want.